So under unavoidable circumstances, I had to switch to a different ISP and was given a different router (AGAIN!) and of course port forwarding doesn't work and I can't host ZDoom games. After some extensive searching and reading actual customer experiences regarding port forwarding with this ISP, it seems that the only way is for me to contact the ISP to "request a public IP" (I don't really know what that is but, okay?).

Now before I go ahead and do this... nevermind the fact that this is inconvenient because customer service on the phone is always shitty and the best way to get anything done is to physically go to their service center which is right in the middle of the city... is this really necessary? I didn't have to do this before with my previous ISP and router and I was able to host ZDoom games and port forward without problems.

There's some critical information you're missing here. You already by process have a public WAN IP, otherwise it would have been impossible for you to have sent that very post. Do you know how your current network is configured and where you internet is bridged from the gateway? Because if you still have a modem, you still have your own gateway and it's at that gateway you need to portforward from. There is very little chance your ISP controls all of that, because pretty much every game and VoIP these days requires some kind of control over its own NAT (without absolutely hammering a TURN server).